“That means that any stimulus money used to cover payroll will be included in the jobs credited to the program, including pay raises for existing employees and pay for people who never were in jeopardy of losing their positions.”

When you have the government pump borrowed money into the economy, don’t forget that in the act of borrowing you are also withdrawing that same amount of money from the economy. $X in and at the same time $X out. You only improve things if the money withdrawn is put back in a more productive use than it would have been put by those who loaned the money– and sufficiently more productive to more than cover the interest bill for the borrowing. You can’t make the water rise in a swimming pool by taking buckets of water out of one end, and then dumping them back in at the other end.